Remark 3.7 If there is no optimal control to (REF )-(REF ), then one can only obtain (REF ) instead of (REF ),
which implies that \(u^{m}(\cdot )\)  is a \(\delta ^{\frac{1}{2}}\) -optimal control as long as \(m \ge N_{\delta }\) . Please refer to [1]} for the details about the near-optimal controls.

